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Related papers: On a Reversible Gray-Scott Type System from Energe…

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We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…

Analysis of PDEs · Mathematics 2025-07-08 Jasper Hoeksema , Chun Yin Lam , André Schlichting

The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…

Analysis of PDEs · Mathematics 2017-10-11 E. S. Daus , L. Desvillettes , A. Jüngel

By identifying potential composite states that occur in the Sel'kov-Gray-Scott (GS) model, we show that it can be considered as an effective theory at large spatio-temporal scales, arising from a more \textit{fundamental} theory (which…

Statistical Mechanics · Physics 2013-10-24 Fred Cooper , Gourab Ghoshal , Alec Pawling , Juan Pérez Mercader

This paper considers quadratic and super-quadratic reaction-diffusion systems for reversible chemistry, for which all species satisfy uniform-in-time $L^1$ a-priori estimates, for instance, as a consequence of suitable mass conservation…

Analysis of PDEs · Mathematics 2015-11-26 Klemens Fellner , Evangelos Latos , Takashi Suzuki

The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…

Analysis of PDEs · Mathematics 2017-11-07 Xiuqing Chen , Ansgar Jüngel

This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

Numerical Analysis · Mathematics 2020-08-26 Barbara Kaltenbacher , William Rundell

The Gray-Scott model can be thought of as an effective theory at large spatiotemporal scales coming from a more fundamental theory valid at shorter spatiotemporal scales. The more fundamental theory includes a composite molecule which is…

Statistical Mechanics · Physics 2019-10-16 John F. Dawson , Fred Cooper , Bogdan Mihaila

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient…

Analysis of PDEs · Mathematics 2018-10-16 Jan Haskovec , Sabine Hittmeir , Peter Markowich , Alexander Mielke

We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…

Analysis of PDEs · Mathematics 2017-03-03 Julian Fischer

In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a…

Statistical Mechanics · Physics 2022-07-13 Aldo Ledesma-Durán , Iván Santamaría-Holek

In this article, we carry out a study of long-term behavior of reaction-diffusion systems augmented with self- and cross-diffusion, using an augmented Gray-Scott system as a general example. The methodology remains generic, and is therefore…

Pattern Formation and Solitons · Physics 2023-08-16 Benjamin Aymard

Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects in a way that total charge and energy are conserved. The…

Analysis of PDEs · Mathematics 2026-04-09 Katharina Hopf , Michael Kniely , Alexander Mielke

We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the…

Analysis of PDEs · Mathematics 2022-02-11 Julian Fischer , Katharina Hopf , Michael Kniely , Alexander Mielke

The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…

Analysis of PDEs · Mathematics 2016-11-11 Laurent Desvillettes , Klemens Fellner , Bao Quoc Tang

We consider a model system consisting of two reaction-diffusion equations, where one species diffuses in a volume while the other species diffuses on the surface which surrounds the volume. The two equations are coupled via a nonlinear…

Analysis of PDEs · Mathematics 2017-07-21 Tang Quoc Bao , Klemens Fellner , Evangelos Latos

We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…

Analysis of PDEs · Mathematics 2022-06-14 Mohamed Majdoub , Nasser-eddine Tatar

On the standard microscopic model of friction we confirm the common belief that the irreversible entropy production originates from the increase of Shannon information. We reveal that the reversible microscopic dynamics would continuously…

Chemical Physics · Physics 2016-09-08 Lajos Diosi

In stochastic thermodynamics, the entropy production of a thermodynamic system is defined by the irreversibility measured by the logarithm of the ratio of the path probabilities in the forward and reverse processes. We derive the relation…

Statistical Mechanics · Physics 2018-03-14 Hyun-Myung Chun , Jae Dong Noh

For many real physico-chemical complex systems detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and heterogeneous catalytic oxidation. Most complex enzyme reactions…

Statistical Mechanics · Physics 2013-01-17 A. N. Gorban , E. M. Mirkes , G. S. Yablonsky

Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct…

Statistical Mechanics · Physics 2009-10-31 L. Rondoni , E. G. D. Cohen